Supplement: Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish

Patrycja Strycharczuk, Małgorzata Ćavar, Stefano Coretta

1 Overview

This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.

The following sections illustrate:

  1. The articulatory data normalisation procedure.
  2. Descriptive plots of the raw data.
  3. Code and plots of the linear regression models.
  4. Summaries of the models in 3.
  5. Extra analyses of F0 and F3.

Only relevant R code is shown in this document. The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.

2 Normalisation procedure

This is Figure 1 from the paper, which illustrates the normalisation procedure. See paper for details.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

3 Descriptive statistics plots

3.1 Articulatory undershoot

Tongue contours from ultrasound tongue imaging of speaker PL01. Tongue tip on the right.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

3.2 Duration

Figure 2 from the paper with boxplots and means of vowel duration depending on speech rate and stress.

3.3 Vowel space

3.3.1 Acoustic vowel space

3.3.2 Articulatory vowel space

3.3.3 Save

4 Inferential statistics

4.1 VIF (multicollinearity)

VIF values below 3 indicate absence of multicollinearity (Zuur, Ieno, and Elphick 2010). For all predictors, VIF < 3.

##   Variables      VIF
## 1  duration 2.169934
## 2      f1.z 1.379401
## 3      f2.z 1.208097
## 4      f0.z 1.122029
## 5      rate 1.639475
## 6    stress 1.451903

4.2 Duration

4.3 F1

4.4 F2

4.5 Z1

4.6 Z2

4.7 Composite plot

5 Model summaries

5.1 Duration

  duration.log
Predictors Estimates CI p
(Intercept) 3.77 3.63 – 3.91 <0.001
rate [normal] 0.19 0.09 – 0.30 <0.001
rate [slow] 0.45 0.31 – 0.59 <0.001
V11 0.14 0.02 – 0.27 0.023
V12 -0.01 -0.16 – 0.14 0.913
V13 0.00 -0.16 – 0.17 0.968
V14 0.00 -0.12 – 0.13 0.955
V15 -0.22 -0.39 – -0.06 0.008
stress [stressed] 0.23 0.18 – 0.28 <0.001
rate [normal] * V11 -0.01 -0.09 – 0.07 0.786
rate [slow] * V11 -0.04 -0.12 – 0.03 0.268
rate [normal] * V12 -0.01 -0.09 – 0.07 0.780
rate [slow] * V12 0.00 -0.08 – 0.08 0.960
rate [normal] * V13 0.05 -0.03 – 0.13 0.182
rate [slow] * V13 -0.02 -0.10 – 0.06 0.576
rate [normal] * V14 -0.01 -0.08 – 0.07 0.901
rate [slow] * V14 0.02 -0.06 – 0.10 0.593
rate [normal] * V15 -0.04 -0.12 – 0.04 0.308
rate [slow] * V15 0.01 -0.07 – 0.08 0.899
rate [normal] * stress
[stressed]
0.15 0.10 – 0.20 <0.001
rate [slow] * stress
[stressed]
0.18 0.13 – 0.23 <0.001
V11 * stress [stressed] 0.12 0.04 – 0.20 0.003
V12 * stress [stressed] -0.05 -0.13 – 0.03 0.215
V13 * stress [stressed] -0.07 -0.15 – 0.00 0.065
V14 * stress [stressed] 0.03 -0.05 – 0.11 0.473
V15 * stress [stressed] -0.01 -0.09 – 0.07 0.841
(rate [normal] * V11) *
stress [stressed]
-0.03 -0.14 – 0.09 0.655
(rate [slow] * V11) *
stress [stressed]
-0.06 -0.17 – 0.06 0.331
(rate [normal] * V12) *
stress [stressed]
-0.04 -0.15 – 0.07 0.465
(rate [slow] * V12) *
stress [stressed]
-0.04 -0.16 – 0.07 0.455
(rate [normal] * V13) *
stress [stressed]
-0.07 -0.18 – 0.04 0.209
(rate [slow] * V13) *
stress [stressed]
-0.08 -0.19 – 0.03 0.173
(rate [normal] * V14) *
stress [stressed]
0.00 -0.11 – 0.11 0.977
(rate [slow] * V14) *
stress [stressed]
0.03 -0.08 – 0.15 0.555
(rate [normal] * V15) *
stress [stressed]
0.12 0.01 – 0.23 0.040
(rate [slow] * V15) *
stress [stressed]
0.11 0.00 – 0.23 0.046
Random Effects
σ2 0.04
τ00 frame 0.02
τ00 speaker 0.04
τ11 speaker.ratenormal 0.03
τ11 speaker.rateslow 0.05
τ11 speaker.stressstressed 0.00
ρ01 speaker.ratenormal -0.81
ρ01 speaker.rateslow -0.78
ρ01 speaker.stressstressed -0.48
N speaker 10
N frame 12
Observations 1440
Marginal R2 / Conditional R2 0.706 / NA

5.2 F1

  f1.z
Predictors Estimates CI p
(Intercept) -0.59 -0.78 – -0.41 <0.001
V11 0.38 0.04 – 0.72 0.029
V12 0.08 -0.29 – 0.46 0.660
V13 -0.29 -0.69 – 0.12 0.163
V14 0.31 -0.02 – 0.64 0.064
V15 -0.49 -0.90 – -0.08 0.020
duration 0.01 0.01 – 0.01 <0.001
stress [stressed] 0.40 0.24 – 0.56 <0.001
V11 * duration 0.02 0.01 – 0.02 <0.001
V12 * duration -0.00 -0.00 – 0.00 0.710
V13 * duration -0.01 -0.01 – -0.01 <0.001
V14 * duration -0.00 -0.01 – 0.00 0.180
V15 * duration 0.00 -0.00 – 0.01 0.476
V11 * stress [stressed] 0.41 0.06 – 0.76 0.022
V12 * stress [stressed] -0.22 -0.54 – 0.09 0.165
V13 * stress [stressed] -0.25 -0.55 – 0.05 0.100
V14 * stress [stressed] 0.16 -0.15 – 0.47 0.307
V15 * stress [stressed] 0.18 -0.13 – 0.50 0.246
duration * stress
[stressed]
-0.00 -0.01 – -0.00 0.005
(V11 * duration) * stress
[stressed]
-0.01 -0.01 – -0.00 0.024
(V12 * duration) * stress
[stressed]
0.01 0.00 – 0.01 0.007
(V13 * duration) * stress
[stressed]
0.00 -0.00 – 0.01 0.608
(V14 * duration) * stress
[stressed]
0.00 -0.00 – 0.01 0.692
(V15 * duration) * stress
[stressed]
-0.01 -0.01 – -0.00 0.019
Random Effects
σ2 0.17
τ00 frame 0.07
τ00 speaker 0.00
τ11 speaker.stressstressed 0.01
ρ01 speaker -1.00
N speaker 10
N frame 12
Observations 1440
Marginal R2 / Conditional R2 0.837 / NA

5.3 F2

  f2.z
Predictors Estimates CI p
(Intercept) -0.06 -0.24 – 0.13 0.550
V11 -0.38 -0.69 – -0.07 0.015
V12 0.28 -0.08 – 0.63 0.132
V13 1.17 0.77 – 1.57 <0.001
V14 -0.52 -0.82 – -0.22 0.001
V15 -0.67 -1.08 – -0.27 0.001
duration 0.00 -0.00 – 0.00 0.283
stress [stressed] 0.05 -0.05 – 0.15 0.332
V11 * duration 0.00 -0.00 – 0.00 0.426
V12 * duration 0.00 -0.00 – 0.01 0.067
V13 * duration 0.01 0.00 – 0.01 <0.001
V14 * duration -0.01 -0.01 – -0.00 <0.001
V15 * duration -0.01 -0.01 – -0.00 0.002
V11 * stress [stressed] 0.04 -0.21 – 0.29 0.765
V12 * stress [stressed] -0.02 -0.25 – 0.20 0.843
V13 * stress [stressed] 0.29 0.08 – 0.51 0.008
V14 * stress [stressed] -0.12 -0.34 – 0.10 0.269
V15 * stress [stressed] -0.26 -0.48 – -0.03 0.025
duration * stress
[stressed]
-0.00 -0.00 – 0.00 0.600
(V11 * duration) * stress
[stressed]
-0.00 -0.00 – 0.00 0.630
(V12 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.858
(V13 * duration) * stress
[stressed]
-0.00 -0.01 – 0.00 0.155
(V14 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.382
(V15 * duration) * stress
[stressed]
0.00 -0.00 – 0.01 0.566
Random Effects
σ2 0.09
τ00 frame 0.08
τ00 speaker 0.00
τ11 speaker.stressstressed 0.00
ρ01 speaker  
N speaker 10
N frame 12
Observations 1440
Marginal R2 / Conditional R2 0.908 / NA

5.4 Z1

  z1
Predictors Estimates CI p
(Intercept) -0.27 -0.41 – -0.13 <0.001
V11 0.17 -0.09 – 0.43 0.211
V12 -0.16 -0.44 – 0.12 0.256
V13 -0.55 -0.85 – -0.26 <0.001
V14 0.25 0.00 – 0.51 0.048
V15 0.12 -0.19 – 0.42 0.453
duration 0.00 0.00 – 0.01 <0.001
stress [stressed] -0.02 -0.15 – 0.11 0.801
V11 * duration 0.01 0.00 – 0.01 <0.001
V12 * duration -0.00 -0.00 – 0.00 0.859
V13 * duration -0.01 -0.01 – -0.00 0.001
V14 * duration 0.01 0.00 – 0.01 0.002
V15 * duration -0.00 -0.01 – 0.00 0.277
V11 * stress [stressed] -0.06 -0.35 – 0.23 0.697
V12 * stress [stressed] 0.07 -0.19 – 0.33 0.591
V13 * stress [stressed] -0.09 -0.34 – 0.16 0.490
V14 * stress [stressed] 0.03 -0.22 – 0.29 0.807
V15 * stress [stressed] 0.04 -0.21 – 0.30 0.737
duration * stress
[stressed]
-0.00 -0.00 – 0.00 0.619
(V11 * duration) * stress
[stressed]
-0.00 -0.00 – 0.00 0.722
(V12 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.952
(V13 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.544
(V14 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.891
(V15 * duration) * stress
[stressed]
-0.00 -0.01 – 0.00 0.591
Random Effects
σ2 0.12
τ00 frame 0.03
τ00 speaker 0.00
τ11 speaker.stressstressed 0.01
ρ01 speaker -1.00
N speaker 10
N frame 12
Observations 1440
Marginal R2 / Conditional R2 0.734 / NA

5.5 Z2

  z2
Predictors Estimates CI p
(Intercept) 0.13 -0.11 – 0.37 0.298
V11 -0.27 -0.66 – 0.12 0.182
V12 0.33 -0.14 – 0.79 0.169
V13 1.09 0.57 – 1.62 <0.001
V14 -0.53 -0.92 – -0.15 0.007
V15 -0.59 -1.12 – -0.06 0.030
duration -0.00 -0.00 – -0.00 0.004
stress [stressed] -0.04 -0.15 – 0.06 0.406
V11 * duration -0.00 -0.00 – 0.00 0.650
V12 * duration 0.00 -0.00 – 0.00 0.607
V13 * duration 0.00 0.00 – 0.01 0.002
V14 * duration -0.00 -0.01 – -0.00 0.005
V15 * duration -0.01 -0.01 – -0.00 0.007
V11 * stress [stressed] 0.09 -0.17 – 0.35 0.487
V12 * stress [stressed] -0.09 -0.32 – 0.14 0.466
V13 * stress [stressed] 0.02 -0.20 – 0.24 0.852
V14 * stress [stressed] 0.09 -0.14 – 0.31 0.457
V15 * stress [stressed] -0.19 -0.42 – 0.04 0.104
duration * stress
[stressed]
0.00 -0.00 – 0.00 0.270
(V11 * duration) * stress
[stressed]
-0.00 -0.01 – 0.00 0.326
(V12 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.779
(V13 * duration) * stress
[stressed]
0.00 -0.00 – 0.00 0.658
(V14 * duration) * stress
[stressed]
-0.00 -0.01 – 0.00 0.312
(V15 * duration) * stress
[stressed]
0.00 -0.00 – 0.01 0.114
Random Effects
σ2 0.09
τ00 frame 0.15
τ00 speaker 0.00
τ11 speaker.stressstressed 0.00
ρ01 speaker  
N speaker 10
N frame 12
Observations 1440
Marginal R2 / Conditional R2 0.874 / NA

6 Further exploratory analyses

6.1 F0

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning: Removed 4 rows containing missing values (geom_point).
  f0.z
Predictors Estimates CI p
(Intercept) -0.93 -1.30 – -0.55 <0.001
V11 0.30 -0.18 – 0.77 0.217
V12 -0.21 -0.67 – 0.24 0.361
V13 0.07 -0.37 – 0.51 0.747
V14 -0.04 -0.48 – 0.40 0.853
V15 0.13 -0.35 – 0.60 0.595
duration 0.01 0.01 – 0.02 <0.001
stress [stressed] 0.81 0.11 – 1.51 0.023
V11 * duration -0.01 -0.02 – -0.00 0.005
V12 * duration 0.00 -0.01 – 0.01 0.802
V13 * duration -0.00 -0.01 – 0.00 0.591
V14 * duration -0.00 -0.01 – 0.01 0.639
V15 * duration 0.01 0.00 – 0.02 0.013
V11 * stress [stressed] -0.28 -0.91 – 0.35 0.379
V12 * stress [stressed] 0.42 -0.14 – 0.98 0.142
V13 * stress [stressed] -0.28 -0.81 – 0.26 0.311
V14 * stress [stressed] 0.01 -0.54 – 0.56 0.966
V15 * stress [stressed] 0.31 -0.24 – 0.87 0.268
duration * stress
[stressed]
-0.01 -0.01 – -0.00 <0.001
(V11 * duration) * stress
[stressed]
0.01 -0.00 – 0.01 0.218
(V12 * duration) * stress
[stressed]
-0.01 -0.02 – 0.00 0.091
(V13 * duration) * stress
[stressed]
0.01 -0.00 – 0.01 0.190
(V14 * duration) * stress
[stressed]
0.00 -0.01 – 0.01 0.938
(V15 * duration) * stress
[stressed]
-0.01 -0.02 – 0.00 0.194
Random Effects
σ2 0.54
τ00 frame 0.03
τ00 speaker 0.24
τ11 speaker.stressstressed 1.11
ρ01 speaker -1.00
N speaker 10
N frame 12
Observations 1436
Marginal R2 / Conditional R2 0.257 / NA

6.2 F3

## `geom_smooth()` using formula 'y ~ x'

7 Session info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.3 (2020-10-10)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Europe/Berlin               
##  date     2021-03-31                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
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##  P statmod        1.4.35     2020-10-19 [?]
##  P stringi        1.5.3      2020-09-09 [?]
##  P stringr      * 1.4.0      2019-02-10 [?]
##  P survey         4.0        2020-04-03 [?]
##  P survival       3.2-10     2021-03-16 [?]
##  P testthat       3.0.2      2021-02-14 [?]
##  P tibble       * 3.1.0      2021-02-25 [?]
##  P tidyr        * 1.1.3      2021-03-03 [?]
##  P tidyselect     1.1.0      2020-05-11 [?]
##  P tidyverse    * 1.3.0      2019-11-21 [?]
##  P usdm         * 1.1-18     2017-06-25 [?]
##  P usethis        2.0.1      2021-02-10 [?]
##  P utf8           1.2.1      2021-03-12 [?]
##  P vctrs          0.3.6      2020-12-17 [?]
##  P withr          2.4.1      2021-01-26 [?]
##  P xfun           0.22       2021-03-11 [?]
##  P xml2           1.3.2      2020-04-23 [?]
##  P xtable         1.8-4      2019-04-21 [?]
##  P yaml           2.2.1      2020-02-01 [?]
##  P zip            2.1.1      2020-08-27 [?]
##  source                                   
##  CRAN (R 4.0.2)                           
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##  CRAN (R 4.0.2)                           
##  CRAN (R 4.0.2)                           
##  Github (stefanocoretta/rticulate@7e8ec81)
##  CRAN (R 4.0.3)                           
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##  CRAN (R 4.0.2)                           
##  CRAN (R 4.0.2)                           
##  CRAN (R 4.0.2)                           
## 
## [1] /Users/ste/repos/polish-reduction/renv/library/R-4.0/x86_64-apple-darwin17.0
## [2] /private/var/folders/yj/b5zvw9lj2zg6tp920wyg14y80000gn/T/RtmpWsGWyS/renv-system-library
## [3] /Library/Frameworks/R.framework/Versions/4.0/Resources/site-library
## [4] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
## 
##  P ── Loaded and on-disk path mismatch.
Zuur, Alain F., Elena N. Ieno, and Chris S. Elphick. 2010. “A Protocol for Data Exploration to Avoid Common Statistical Problems.” Methods in Ecology and Evolution 1 (1): 3–14. https://doi.org/10.1111/j.2041-210X.2009.00001.x.